Sausage Gravy and Eggs Hash Brown Skillet Recipe

1 Tablespoon vegetable oil
½ yellow onion, finely chopped
½ red bell pepper, finely chopped
½ green bell pepper, finely chopped
4 ounces mushrooms, finely chopped
14 ounces (1/2 bag) frozen hash browns
6 eggs
Salt and Pepper

For the sausage gravy:

1 lb. ground breakfast sausage
3 Tablespoons grease from the sausage (or butter)
3 Tablespoons all purpose flour
2 cups whole milk